How to apply an image texture on a cylinder
A UV map is a 2D representation of a 3D object. 

The name UV map is derived from its axis’. In 3D space, x y and z is used to represent the dimensions of width, depth and height respectively. When we go to a 2D plane, instead of using xy, we use uv as shown below.




If you unfolded a cardboard box and laid it out flat, that is a representation of your cubes surface area.

Blender uses this 2D mesh to allow texturing.  By colouring in the faces of the unwrapped mesh, blender will project that image onto the respective face on your mesh.



If you leave blender to unwrap the mesh itself, stretching can occur. This is when a rectangular face is unwrapped into a square face, or vice versa. This most often occurs when your objects geometry is unbalanced.

To fix this, select your object and go into edit mode. Select everything and press control-u and choose smart uv unwrap. Press ok on the pop up window. 

In the image viewer, you should now see your mesh presented in 2D.

If the 2D mesh does not look proportionally correct to your object, you will need to apply the scale.

Blender has two ways of storing it’s dimensional size data. One is the each axis’ length which is the true size and the other is the objects dimensions which is used for accurate scaling and uv mapping. If you scale your mesh on one axis or extrude or extend it in any form, the dimensions change on one axis only.

For example; we have a cube 5x5x5 units and dimensions of 1x1x2. When blender tries to unwrap it, it will stretch any face that had an z direction. So your cube will have four sides twice as long as the others. Try it  in blender to gain a better understanding.



Note how the faces on the UV in the image editor look like they are all in the same proportion and on the object they aren't, stretching the texture

To fix this, go to object mode and select your item. Go to object->apply->scale. Fixed. You may need to go through the uv unwrapping process again.

Here is the quad with correct UV unwrapping:



Quick tip:

If you have multiple objects that require uv unwrapping, do it to one object then select the rest. Set the active object to the object you just UV unwrapped and hit control L. Chose object data.

Tada. Magic.

Good luck with your project and I hope I helped,

BFB